It's official: the notorious Higgs boson has been discovered at the Large Hadron Collider at CERN. The Higgs is a subatomic particle whose existence was predicted by theoretical physics. Also termed the god particle, the Higgs boson is said to have given other particles their mass. But how did it do that? In this two-part article we explore the so-called Higgs mechanism, starting with the humble bar magnet and ending with a dramatic transformation of the early Universe.

Infinity is a pain. Its paradoxes easily ensnare the unsuspecting reasoner. So over the centuries, mathematicians have carefully constructed bulwarks against its predations. But now cosmologists have developed theories that put them squarely outside the mathematicians' "green zone" of safety.

Quantum mechanics and general relativity are incompatible — and this has led to a decades-long search for a theory of quantum gravity that could combine the two. But the particle physicist Richard Woodard thinks that the mismatch between the two could be nothing more than an illusion, created by the complicated maths techniques used in attempts to unite them.

John Barrow gives us an overview, from Aristotle's ideas to Cantor's never-ending tower of mathematical infinities, and from shock waves to black holes.

Remember Frank Lampard's disallowed goal in the 2010 World Cup match against Germany? The ball hit the crossbar, landed well behind the line but then bounced out again. And it all happened too quickly for the ref to spot it was a goal. How these kind of (non)-goals happen and what can we do about them?

Horses, like all animals, have a number of different gaits. But how can they perform these complicated leg movements without having to stop and think? And why do they switch to a new gait when they want to go faster? Mathematics can shed some light on these questions.

A simple question to ask about kayak races is whether having lots of paddlers helps or slows the boat down? The kayak with two paddlers has twice as many "engines" to power it but it also has twice as much weight to drag through the water. Which is the dominant factor?

It does pay to be nice if you repeatedly deal with the same person. Martin Nowak explains why cooperation also wins in matters of reputation, neighbourliness and family. But can evolutionary game theory save the world?

The holy grail for 21st century physics is to produce a unified theory of everything that can describe the world at every level, from the tiniest particles to the largest galaxies. Currently the strongest contender for such a theory is something called M-theory. So what is this supposed mother of all theories all about?

The men's and women's 100 metre freestyle swimming races are set to be two of the most glamorous events of the London 2012 Olympic Games. Much has been made of the swimming events for London 2012 because the previous 2008 Beijing Olympics saw an unprecedented number of new world records, due to the use of controversial swimsuits. So how do these suits improve performance?

A recent study from Harvard reported that eating red meat is associated with a 13% increased risk of death. But what does this mean? Surely our risk of death is already 100%, and a risk of 113% does not seem very sensible? To really interpret this number we need to use some maths.